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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 4 — Apr. 1, 2002
  • pp: 702–715

Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis

Elias N. Glytsis  »View Author Affiliations


JOSA A, Vol. 19, Issue 4, pp. 702-715 (2002)
http://dx.doi.org/10.1364/JOSAA.19.000702


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Abstract

The range of validity of the scalar diffraction analysis is quantified for the case of two-dimensionally-periodic diffractive optical elements (crossed gratings). Three canonical classes of two-dimensionally-periodic grating structures are analyzed by using the rigorous coupled-wave analysis as well as the scalar diffraction analysis. In all cases the scalar-analysis diffraction efficiencies are compared with the exact diffraction efficiencies. The error in using the scalar analysis is then determined as a function of the grating-period(s)-to-wavelength ratio(s), the minimum feature size, the grating depth, the refractive index of the grating, the incident polarization, and the number of phase levels. The three classes of two-dimensional (2-D) unit cells are as follows: (1) a rectangular pillar, (2) an elliptical pillar, and (3) an arbitrarily pixellated multilevel 2-D unit cell that is representative of more complicated diffractive optical elements such as computer-generated holograms. In all cases a normally incident electromagnetic plane wave is considered. It is shown that the error of the scalar diffraction analysis in the case of two-dimensionally-periodic diffractive optical elements is greater than that for the corresponding one-dimensionally-periodic counterparts. In addition, the accuracy of the scalar diffraction analysis degrades with increasing refractive index, grating thickness, and asymmetry of the 2-D unit cell and with decreasing grating-period-to-wavelength ratio and feature size.

© 2002 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1380) Diffraction and gratings : Binary optics
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: April 25, 2001
Revised Manuscript: July 25, 2001
Manuscript Accepted: September 13, 2001
Published: April 1, 2002

Citation
Elias N. Glytsis, "Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis," J. Opt. Soc. Am. A 19, 702-715 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-4-702

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